Romeo and Juliet (ballet) opens at the Kauffman Center sometime around Valentine's Day. Should be wonderful and you can eat at The Webster House next to it for a fantastic meal.
Ice Skating at Crown Center? I recently went alone with my best friend and it was so nice to skate upright - not having to hold our little kids' hands! You could always dine before/after at a restaurant nearby. There are plenty in every price range. Lulu's new space just off 19th Street is a lot bigger than it used to be.
How about an independent film at the Tivoli or Glenwood?
Not fancy or destination-y, but Chai Shai on 59th (near Holmes) has wonderful food with a charming atmosphere. And it's pretty affordable.
How about sitting in the hot tub at Matt Ross (downtown OP)? It's the best part of the indoor pool and my husband and I have to do it in shifts since our kiddo is only 4 and shouldn't be in it. We'd love the chance to relax together.
I have not been to Justus Drugstore in Smithville because I hear it is very pricey, but have also heard it's THE special occasion destination.
A stroll in the JoCo Arboretum (esp. the birdhouse section) could be quite romantic without kiddos. Actually, you can make anything romantic without kids, even bowling.
The Kemper Museum is free and their restaurant is wonderful. So not free, though. :)
I second the World War I museum. It is an amazing experience! Pair it with dinner at Lidia's for something close by.
Perhaps the KC Culinary School is offering a session that week?
Oh and my favorite art supply store is Utrecht on Main Street.